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Register a new userOn the Planckian bound for heat diffusion in insulators
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High temperature thermal transport in insulators has been conjectured to be subject to a Planckian bound on the transport lifetime $tau gtrsim tau_text{Pl} equiv hbar/(k_B T)$, despite phonon dynamics being entirely classical at these temperatures. We argue that this Planckian bound is due to a quantum mechanical bound on the sound velocity: $v_s < v_M$. The `melting velocity $v_M$ is defined in terms of the melting temperature of the crystal, the interatomic spacing and Plancks constant. We show that for several classes of insulating crystals, both simple and complex, $tau/tau_text{Pl} approx v_M/v_s$ at high temperatures. The velocity bound therefore implies the Planckian bound.
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It has been known for decades that thermal conductivity of insulating crystals becomes proportional to the inverse of temperature when the latter is comparable to or higher than the Debye temperature. This behavior has been understood as resulting from Umklapp scattering among phonons. We put under scrutiny the magnitude of the thermal diffusion constant in this regime and find that it does not fall below a threshold set by the square of sound velocity times the Planckian time ($tau_p=hbar/k_BT$). The conclusion, based on scrutinizing the ratio in cubic crystals with high thermal resistivity, appears to hold even in glasses where Umklapp events are not conceivable. Explaining this boundary, reminiscent of a recently-noticed limit for charge transport in metals, is a challenge to theory.
We study current-induced step bunching and wandering instabilities with subsequent pattern formations on vicinal surfaces. A novel two-region diffusion model is developed, where we assume that there are different diffusion rates on terraces and in a small region around a step, generally arising from local differences in surface reconstruction. We determine the steady state solutions for a uniform train of straight steps, from which step bunching and in-phase wandering instabilities are deduced. The physically suggestive parameters of the two-region model are then mapped to the effective parameters in the usual sharp step models. Interestingly, a negative kinetic coefficient results when the diffusion in the step region is faster than on terraces. A consistent physical picture of current-induced instabilities on Si(111) is suggested based on the results of linear stability analysis. In this picture the step wandering instability is driven by step edge diffusion and is not of the Mullins-Sekerka type. Step bunching and wandering patterns at longer times are determined numerically by solving a set of coupled equations relating the velocity of a step to local properties of the step and its neighbors. We use a geometric representation of the step to derive a nonlinear evolution equation describing step wandering, which can explain experimental results where the peaks of the wandering steps align with the direction of the driving field.
We have used the indium/copper surface alloy to study the dynamics of surface vacancies on the Cu(001) surface. Individual indium atoms that are embedded within the first layer of the crystal, are used as probes to detect the rapid diffusion of surface vacancies. STM measurements show that these indium atoms make multi-lattice-spacing jumps separated by long time intervals. Temperature dependent waiting time distributions show that the creation and diffusion of thermal vacancies form an Arrhenius type process with individual long jumps being caused by one vacancy only. The length of the long jumps is shown to depend on the specific location of the indium atom and is directly related to the lifetime of vacancies at these sites on the surface. This observation is used to expose the role of step edges as emitting and absorbing boundaries for vacancies.
It has recently been conjectured that the transport relaxation rate in metals is bounded above by the temperature of the system. In this work, we discuss the transport phenomenology of overdoped electron-doped cuprates, which we show constitute an unambiguous counterexample to this putative Planckian bound, raising serious questions about the efficacy of the bound.
Cuprous oxide (Cu2O) films from 25 nm to 1500 nm were electrodeposited on n-Si(100) and Ni/n-Si(100) substrates from aqueous solution at room temperature. X-ray diffraction and transmission electron microscopy imaging show that the Cu2O structure and morphology is strongly affected by the substrate choice, with V shape and U shape columnar growth on n-Si(100) and Ni/n-Si(100), respectively. Atomic force microscopy reveals the presence of rounded grains at the surface in both cases. Anomalous and normal roughening are observed in films grown on n-Si and Ni, respectively, but estimates of scaling exponents are not conclusive. On the other hand, the distributions of local heights, roughness, and extremal heights show good agreement with those of the fourth order linear stochastic equation of Mullins and Herring (MH). Thus, surface dynamics in both systems is dominated by diffusion of adsorbed molecules, with no large scale effect of possible inhomogeneities in mass flux from the solution or in reaction and adsorption rates. In growth on n-Si substrates, the noise amplitude of the MH equation increases in time as t^{0.8}, while the coefficient of the curvature-related term is time-independent. Step edge energy barriers restrict the mass flux across grain boundaries, thus a broad size distribution of initial grains leads to coarsening of the larger ones. This explains their V shape in the thickest films and establishes a connection with the anomalous roughening. These effects are reduced in films grown on Ni/n-Si, which initially have much larger grains with narrower size distributions and, consequently, smaller fluctuations in coarse grained growth rates.
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